Unfortunately, some folks on the rightist end of libertarianism, anarcho-capitalism, or “anarchism of the right” have been veering off into this neo-reactionary, nostalgic monarchist, or neo-fascist stuff just as some on the left end of anarchism and libertarianism have veered off into social democracy (Chomsky), totalitarian humanism (the antifa anarchists), and cultural Marxism (C4SS). This is an important critique of deviations into authoritarian rightism by Noah Millman.
The American Conservative
First of all, I would distinguish between three arguments for democracy as a political system, because I only really believe in two of them, while pretty thoroughly rejecting the third. But I believe in the two remaining arguments very strongly.
The argument that I reject is the idea that democracy is the only form of government in which the “people’s will” rules – and, as such, is the only legitimate form of government. I don’t believe “the people” have a will (only individuals do), and I don’t think an authority’s legitimacy derives from some kind of fundamental theory. Rather, I take the Burkean view that an authority’s legitimacy is an observed reality and has more to do with longevity than with being derived from any particular principle. As such, a longstanding monarchy is perfectly capable of being a legitimate authority. So is the government of Communist China. So, in a much more tenuous and provisional sense, is the authority of a local Somali or Afghan warlord.
The two arguments for democracy that I strongly endorse come from opposite directions, but are complementary, in my view, not contradictory. The first is the notion that participating in the process of self-government is elevating in and of itself, and, as such, every people should aspire to republicanism. What I have in mind is something like Hannah Arendt’s view as articulated in On Revolution. There is a real question whether imperial-scale entities like the United States, or even entities as large as the traditional European nation-states, can achieve this particular republican good, or whether you max out at the scale of a large city-state.